Method for measuring effective temperature inside a sealed container

ABSTRACT

A method of measuring the effective temperature inside a sealed container having a headspace is provided. A liquid solvent is added to the container, and a solid compound is added to the liquid solvent to create a saturated solution. Vapor of the saturated solution is allowed to equilibrate in the headspace of the sealed container, and a volume thereof is transferred to a chromatographic column, where chromatographic readings of the equilibrated vapor are taken. A temperature within the sealed container is then calculated based upon the chromatographic readings of the equilibrated vapor, wherein the temperature calculation is based upon the concentrations of the liquid solvent and the solid compound in the equilibrated vapor.

FIELD OF THE INVENTION

[0001] The present invention relates to a method of analyzing materials,and more particularly, to a method of accurately measuring the effectivetemperature inside a sealed container, such as a headspace vial.

BACKGROUND OF THE INVENTION

[0002] The technique of equilibrium headspace extraction involvesplacing a liquid or solid sample into a suitable sealed vial andallowing volatile analytes within the sample to reach equilibration inconcentration between the sample matrix and the vapor above it (i.e.,the headspace). A fixed volume of the vapor is then transferred to a gaschromatograph for analysis. At equilibration, the concentration of eachanalyte in the headspace is defined by the amount of the analytepresent, the volumes of the two phases and the partition coefficient forthat analyte between the two phases. The partition coefficient, which isa thermodynamic property, is highly dependent on temperature and so mustbe carefully controlled within the instrumentation if good analyticalprecision is to be achieved.

[0003] Current state-of-the-art headspace samplers, such as the modelTurboMatrix Automatic Headspace Sampler distributed by PerkinElmerInstruments LLC, are designed to maintain a very stable vial temperatureby making use of a large thermostatted metal oven block. However,despite the fact that stable vial temperatures can be maintained, anumber of issues regarding temperature control remain.

[0004] For example, the true temperature of the vial may not beaccurately measured. The electronic sensor used to monitor temperatureis typically located within a heating belt that surrounds the oven blockand is remote from the vial. As such, the temperature reading may notreflect the true vial temperature at all settings. Moreover, it ispossible that all vial positions may not be at the same temperature.

[0005] Another issue may arise when a new (cold) vial is inserted intothe oven block. In such a case, there may be a drop in temperature inone or more of the other vials which cannot be readily detected usingknown methods. Furthermore, known methods of temperature measurement maynot take into account the fact that the vial temperature may change overtime.

[0006] Another potential issue is that certain requirements, such as GLP(Good Laboratory Practices) certification standards and FDA (Food andDrug Administration) approval requirements, may require that the vialtemperature be monitored and/or calibrated.

[0007] In addition, some instruments which are not state-of-the-art maybe weak in the area of vial temperature control. As such, it may bedesirable to evaluate the performance of such instruments using a simplemethod for temperature measurement.

[0008] Traditionally, a thermocouple or similar temperature-measuringprobe would be inserted into the vial. However, this technique istedious to perform, interrupts the normal operation of the instrument,and requires special tools. Moreover, taking a reading from a singlepoint inside the vial may not truly reflect the “effective” temperatureof the whole vial. Instead, it would be more desirable to make use of asuitable sample in a vial and use chromatography to determinetemperature—after all, it is this process for which standardization isbeing attempted.

[0009] What is desired, therefore, is a method of measuring theeffective temperature inside a sealed container which accuratelyreflects the true container temperature at all instrument settings,which takes into account temperature variations across various containerpositions, which measures the temperature of each container separatelyfrom other containers when a plurality of containers are used, whichtakes into account the fact that the container temperature may changeover time, which allows for temperature calibration, which can be usedto evaluate the temperature control performance of an instrument, whichis easy to perform, which does not interrupt the normal operation of theinstrument, which does not require special tools, and which useschromatography to determine temperature.

SUMMARY OF THE INVENTION

[0010] Accordingly, it is an object of the present invention to providea method of measuring the effective temperature inside a sealedcontainer which accurately reflects the true container temperature atall instrument settings.

[0011] Another object of the present invention is to provide a method ofmeasuring the effective temperature inside a sealed container having theabove characteristics and which takes into account temperaturevariations across various container positions.

[0012] A further object of the present invention is to provide a methodof measuring the effective temperature inside a sealed container havingthe above characteristics and which measures the temperature of eachcontainer separately from other containers when a plurality ofcontainers are used.

[0013] Still another object of the present invention is to provide amethod of measuring the effective temperature inside a sealed containerhaving the above characteristics and which takes into account the factthat the container temperature may change over time.

[0014] Yet a further object of the present invention is to provide amethod of measuring the effective temperature inside a sealed containerhaving the above characteristics and which allows for temperaturecalibration.

[0015] Still a further object of the present invention is to provide amethod of measuring the effective temperature inside a sealed containerhaving the above characteristics and which can be used to evaluate thetemperature control performance of an instrument.

[0016] Still a further object of the present invention is to provide amethod of measuring the effective temperature inside a sealed containerhaving the above characteristics and which is easy to perform.

[0017] Yet another object of the present invention is to provide amethod of measuring the effective temperature inside a sealed containerhaving the above characteristics and which does not interrupt the normaloperation of the instrument.

[0018] Still a further object of the present invention is to provide amethod of measuring the effective temperature inside a sealed containerhaving the above characteristics and which does not require specialtools.

[0019] Yet still a further object of the present invention is to providea method of measuring the effective temperature inside a sealedcontainer having the above characteristics and which uses chromatographyto determine temperature.

[0020] These and other objects of the present invention are achieved byprovision of method of measuring the effective temperature inside asealed container having a headspace. A liquid solvent is added to thecontainer, and a solid compound is added to the liquid solvent to createa saturated solution. Vapor of the saturated solution is allowed toequilibrate in the headspace of the sealed container, and a volumethereof is transferred to a chromatographic column, wherechromatographic readings of the equilibrated vapor are taken. Atemperature within the sealed container is then calculated based uponthe chromatographic readings of the equilibrated vapor, wherein thetemperature calculation is based upon the concentrations of the liquidsolvent and the solid compound in the equilibrated vapor.

[0021] Preferably, the chromatographic readings comprise readings ofpeak areas of the liquid solvent and the solid compound. Mostpreferably, the calculating step comprises the step of calculating atemperature within the sealed container based upon a ratio of thereadings of peak areas of the liquid solvent and the solid compound.

[0022] In one preferred embodiment, the liquid solvent comprisesn-dodecane and the solid compound comprises naphthalene. In anotherembodiment, the liquid solvent comprises n-octadecane and the solidcompound comprises anthracene.

[0023] The invention and its particular features and advantages willbecome more apparent from the following detailed description consideredwith reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0024]FIG. 1 is a schematic view of a sealed vial for which thetemperature can be measured in accordance with the present invention;

[0025]FIG. 2 is a graphical representation of the ideal vapor pressurebehavior for a binary mixture according to Raoult's Law as employed bythe present invention;

[0026]FIG. 3 is a graphical representation of chromatograms of an-dodecane and naphthalene test mix thermostatted over a range oftemperatures which illustrates a portion of the theory underlying thepresent invention;

[0027]FIG. 4 is a plot of area ratio (naphthalene/n-dodecane) versus settemperature in ° C. which illustrates a portion of the theory underlyingthe present invention; and

[0028]FIG. 5 is a plot of a linear relationship between the areas ofnaphthalene and n-dodecane which illustrates a portion of the theoryunderlying the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0029] In arriving at the present invention, consideration was given tomaking use of temperature dependence of partition coefficients in orderto determine the effective temperature within a vial. In accordance withsuch a method, a solution of two solutes in a suitable solvent would beprepared. The solutes and solvent would be chosen so that theirpartition coefficients exhibited different temperature profiles. Theirrelative concentrations (hence chromatographic peak sizes) would be ameasure of the temperature.

[0030] However, it was found that this approach may be undesirablebecause it would rely on very precise control of concentrations andvolumes. Moreover, the compounds would have to be chemically similar sothat their relative response factors on the GC detector would beconstant, and differences in partition coefficient profiles wouldtherefore be subtle.

[0031] Consideration was also given to making use of temperaturedependence of vapor pressures in order to determine the effectivetemperature within a vial. In accordance with this method, an excess ofa suitable compound disposed in a thermostatted headspace vial wouldsaturate the headspace with compound vapor. The concentration of thevapor at the saturation point would be proportional to the vaporpressure. Vapor pressure is dependent upon temperature and so theconcentration of vapor in the headspace is temperature dependent. Bychoosing two compounds with different vapor pressure curves, the ratioof their concentrations (hence chromatographic peak sizes) would be ameasure of temperature.

[0032] However, it was found that this approach may be undesirablebecause when two compounds are mixed together, there is a change totheir respective vapor pressures that is concentration dependent and soresults are difficult to predict.

[0033] In order to overcome the deficiencies of the prior art and toavoid the concerns expressed with respect to the approaches describedabove, it was decided upon to make use of temperature dependence ofsolubility and vapor pressure.

[0034] Referring to FIG. 1, this method relies on the solubility of asolid compound 10 in a suitable liquid solvent. Sufficient solid 10 isadded to ensure that a saturated solution 12 is produced. The saturationconcentration is highly temperature dependent but should always be thesame at any given temperature. This effect will also mean that theconcentration of both compound vapors in the headspace 14 inside asealed vial 16 containing the saturated solution 12 will also bepredictable at any given temperature. The compound concentrations in theheadspace 14 are now dependent on both liquid solubility and vaporpressure and should give an enhanced temperature effect.

[0035] In one preferred embodiment, naphthalene was chosen as the solidcompound and n-dodecane was chosen as the liquid solvent. Thesecompounds were found to be appropriate for a number reasons, such as thefact that they are both hydrocarbons and should give relative responsefactor reproducibility on all flame ionization detectors. Moreover,n-dodecane becomes saturated with naphthalene at concentrations ofapproximately 30% at ambient temperature, which simplifies the measuringprocess. Furthermore, the vapor pressures of pure n-dodecane and purenaphthalene are similar, they are chromatographically-friendly compoundsthat can be run on almost any column, and their vapor pressure curvesare significantly different.

[0036] However, it should be understood that the combination ofn-dodecane and naphthalene is not meant to be limiting in any way, andthe use of numerous combinations of compounds with the inventivemeasurement method is contemplated. More specifically, experiments haveshown that the use of n-dodecane and naphthalene may be limited totemperatures in the region of about 40 to 70° C. (naphthalene melts at800° C.). For higher temperatures, other compounds, such a combinationof n-octadecane and anthracene, may be used without departing from thepresent invention.

[0037] The general procedure employed with the present inventioninvolves the following steps. First, a vial containing an approximately10-90 mix of n-dodecane and naphthalene is placed into a headspacesampler and allowed to thermostat (i.e., typically for about 20 minutes)at the set temperature. Next, a suitable volume of the equilibratedheadspace vapor is transferred to a chromatographic column fordetermination. Finally, the temperature of the headspace vial is derivedfrom the ratio of the two peak areas, as more fully discussed below.

Theoretical Model

[0038] The vapor pressure of a component in a binary mixture may beconveniently described by Raoult's Law as: $\begin{matrix}{\frac{\left( {p^{0} - p} \right)}{p^{0}} = {x = \frac{n_{2}}{\left( {n_{1} + n_{2}} \right)}}} & (1)\end{matrix}$

[0039] Where:

[0040] p⁰ is the vapor pressure of the compound in the mixture

[0041] p is the vapor pressure of the pure compound

[0042] x is the mole fraction of the compound in the mixture

[0043] n₁ is the number of moles of the other compound

[0044] n₂ is the number of moles of the compound being studied

[0045]FIG. 2, which graphically illustrates the ideal vapor pressurebehavior for a binary mixture according to Raoult's Law, shows how therelative vapor pressure, hence vapor phase concentration, of eachcomponent depends on the concentration of that component in the liquidmixture and the vapor pressure of the pure compound. If the vapor wereto be chromatographed, then the peak area ratio for the two compoundswould be dependent on both their liquid concentrations and pure vaporpressures.

[0046] The concentration of a saturated solution of naphthalene inn-dodecane is temperature dependent and may again be described byanother form of Raoult's Law as: $\begin{matrix}{x = {\frac{n_{2}}{\left( {n_{1} + n_{2}} \right)} = ^{\lbrack{\frac{L_{f}}{R}{(\frac{T_{0} - T}{T_{0} \cdot T})}}\rbrack}}} & (2)\end{matrix}$

[0047] Where:

[0048] L_(f) is the molar heat of fusion

[0049] R is the gas constant

[0050] T₀ is the compound freezing point absolute temperature

[0051] T is the absolute temperature of the solution

[0052] The dependence of vapor pressure of a pure substance ontemperature may be described by the Clapeyron-Clausius Equation as:$\begin{matrix}{p = ^{({\frac{L_{v}}{RT} + C})}} & (3)\end{matrix}$

[0053] Where:

[0054] L_(v) is the molar heat of vaporization

[0055] C is a constant

[0056] It should be noted, however, that in practice, deviations fromEquations 1, 2 and 3 may be expected because of inter-molecular forces.Therefore, these relationships should be used only for guidance.

[0057] Equations 1, 2 and 3 may be combined to give Equations 4 or 5,which relate the predicted vapor pressure, p₀, for a component in asaturated mixture to temperature, T, as follows: $\begin{matrix}{p_{0} = \frac{^{\lbrack{\frac{L_{v}}{RT} + C}\rbrack}}{1 - ^{\lbrack{\frac{L_{f}}{R}{(\frac{T_{0} - T}{T_{0} \cdot T})}}\rbrack}}} & (4)\end{matrix}$

[0058] or $\begin{matrix}{p_{0} = \frac{a \cdot ^{\frac{b}{T}}}{1 - {c \cdot ^{\frac{d}{T}}}}} & (5)\end{matrix}$

[0059] Where:

[0060] a is a constant

[0061] b is a constant

[0062] c is a constant

[0063] d is a constant

[0064] The ratio of the observed vapor pressures would be:$\begin{matrix}{\frac{p_{0}}{p_{0}^{\prime}} = {\frac{a \cdot ^{\frac{b}{T}}}{a^{\prime} \cdot ^{\frac{b^{\prime}}{T}}} \cdot \frac{1 - {c^{\prime} \cdot ^{\frac{d^{\prime}}{T}}}}{1 - {c \cdot ^{\frac{d}{T}}}}}} & (6)\end{matrix}$

[0065] Where:

[0066] P ′ is the predicted vapor pressure for the second compound

[0067] a′ is a constant relating to the second compound

[0068] b′ is a constant relating to the second compound

[0069] c′ is a constant relating to the second compound

[0070] d′ is a constant relating to the second compound

[0071] Equation 6 may be reduced to the final form: $\begin{matrix}{\frac{p_{0}}{p_{0}^{\prime}} = \frac{{a \cdot ^{\frac{b}{T}}} - {c \cdot ^{\frac{d}{T}}}}{1 - {f \cdot ^{\frac{g}{T}}}}} & (7)\end{matrix}$

[0072] Where:

[0073] a is a constant

[0074] b is a constant

[0075] c is a constant

[0076] d is a constant

[0077] f is a constant

[0078] g is a constant

[0079] Because compound concentration and hence chromatographic peakarea is proportional to the vapor pressure, Equation 7 also applies tothe peak area ratio, as described more fully below.

[0080]FIG. 3 shows chromatograms of the n-dodecane and naphthalene testmix thermostatted over a range of temperatures. The experimentalconditions are given in Table 1. FIG. 4 shows a plot of area ratio(naphthalene/n-dodecane to give a positive slope) versus set temperaturein ° C. The non-smoothness in the plot may be caused by errors in themeasurement or may be a true indication of varying vial temperature(readings were taken with different vials, in different carouselpositions and at different times). TABLE 1 Experimental ConditionsChromatograph AutoSystem XL (PerkinElmer Instruments) Column 30 m × 0.32mm × 1.0 μm PE-5 (PerkinElmer Instruments) Oven 200° C. IsothermalCarrier Gas Helium at 12.5 psig with PPC Interface Split injector at250° C. with low dead volume liner Detector FID at 300° C., range ×1,attenuation ×4 Headspace HS40 XL (PerkinElmer Instruments) ThermostatTemp. 44° C. to 72° C. in 4° increments Thermostat Time 20 min. Pressure15 psig with PPC Press Time 1 min. Inject Time 0.02 min. Withdrawal Time0.5 min. Sample 180 mg naphthalene and 20 mg n-dodecane in 22-ml vial

[0081] By inverting the area ratios, the data seems to approximate tothe following simple linear relationship, which is also plotted in FIG.5: $\begin{matrix}{\frac{{Area}_{Dodecane}}{{Area}_{Naphthalene}} = {2.094 - {0.02313 \cdot T}}} & (8)\end{matrix}$

[0082] Thus, solving Equation 8 for T, the temperature of the vial canbe determined by employing a chromatograph to measure the peak areas forn-dodecane and naphthalene.

[0083] The present invention, therefore, provides a method of measuringthe effective temperature inside a sealed container which accuratelyreflects the true container temperature at all instrument settings,which takes into account temperature variations across various containerpositions, which measures the temperature of each container separatelyfrom other containers when a plurality of containers are used, whichtakes into account the fact that the container temperature may changeover time, which allows for temperature calibration, which can be usedto evaluate the temperature control performance of an instrument, whichis easy to perform, which does not interrupt the normal operation of theinstrument, which does not require special tools, and which useschromatography to determine temperature.

[0084] Although the invention has been described with reference to aparticular arrangement of parts, features and the like, these are notintended to exhaust all possible arrangements or features, and indeedmany other modifications and variations will be ascertainable to thoseof skill in the art.

What is claimed is:
 1. A method for determining the effectivetemperature inside a sealed container comprising the steps of: providinga sealed container having a headspace; adding a liquid solvent to thecontainer; adding a solid compound to the liquid solvent to create asaturated solution; allowing vapor of the saturated solution toequilibrate in the headspace of the sealed container; transferring avolume of the equilibrated vapor to a chromatographic column; takingchromatographic readings of the equilibrated vapor; and calculating atemperature within the sealed container based upon the chromatographicreadings of the equilibrated vapor, wherein the temperature calculationis based upon the concentrations of the liquid solvent and the solidcompound in the equilibrated vapor.
 2. The method of claim 1 wherein thechromatographic readings comprise readings of peak areas of the liquidsolvent and the solid compound.
 3. The method of claim 2 wherein saidcalculating step comprises the step of calculating a temperature withinthe sealed container based upon a ratio of the readings of peak areas ofthe liquid solvent and the solid compound.
 4. The method of claim 1wherein the liquid solvent comprises n-dodecane and the solid compoundcomprises naphthalene.
 5. The method of claim 4 wherein said calculatingstep employs the following equation:$\frac{{Area}_{Dodecane}}{{Area}_{Naphthalene}} = {2.094 - {0.02313 \cdot T}}$

wherein Area_(Dodecane) and Area_(Naphthalane) are readings of peakareas of n-dodecane and naphthalene respectively, and T is thetemperature within the sealed container.
 6. The method of claim 1wherein the liquid solvent comprises n-octadecane and the solid compoundcomprises anthracene.
 7. A method for determining the effectivetemperature inside a sealed container comprising the steps of: providinga sealed container having a headspace; adding a liquid solvent to thecontainer; adding a solid compound to the liquid solvent to create asaturated solution; allowing vapor of the saturated solution toequilibrate in the headspace of the sealed container; transferring avolume of the equilibrated vapor to a chromatographic column; takingchromatographic readings of the equilibrated vapor; calculating peakareas of the liquid solvent and the solid compound based upon thechromatographic readings; and calculating a temperature within thesealed container based upon a ratio of the readings of peak areas of theliquid solvent and the solid compound, wherein the temperaturecalculation is based upon the concentrations of the liquid solvent andthe solid compound in the equilibrated vapor, which are dependent uponboth liquid solubility and vapor pressure.
 8. The method of claim 7wherein the liquid solvent comprises n-dodecane and the solid compoundcomprises naphthalene.
 9. The method of claim 8 wherein said calculatingstep employs the following equation:$\frac{{Area}_{Dodecane}}{{Area}_{Naphthalene}} = {2.094 - {0.02313 \cdot T}}$

wherein Area_(Dodecane) and Area_(Naphthalane) are readings of peakareas of n-dodecane and naphthalene respectively, and T is thetemperature within the sealed container.
 10. The method of claim 7wherein the liquid solvent comprises n-octadecane and the solid compoundcomprises anthracene.
 11. A method for determining the temperature of asaturated solution comprising the steps of: mixing a liquid solvent witha solid compound to create a saturated solution; allowing vapor of thesaturated solution to equilibrate; taking chromatographic readings ofthe equilibrated vapor; calculating peak areas of the liquid solvent andthe solid compound based upon the chromatographic readings; andcalculating a temperature of the saturated solution based upon a ratioof the readings of peak areas of the liquid solvent and the solidcompound, wherein the temperature calculation is based upon theconcentrations of the liquid solvent and the solid compound in theequilibrated vapor, which are dependent upon both liquid solubility andvapor pressure.
 12. The method of claim 11 wherein the liquid solventcomprises n-dodecane and the solid compound comprises naphthalene. 13.The method of claim 12 wherein said calculating step employs thefollowing equation:$\frac{{Area}_{Dodecane}}{{Area}_{Naphthalene}} = {2.094 - {0.02313 \cdot T}}$

wherein Area_(Dodecane) and Area_(Naphthalane) are readings of peakareas of n-dodecane and naphthalene respectively, and T is thetemperature within the sealed container.
 14. The method of claim 11wherein the liquid solvent comprises n-octadecane and the solid compoundcomprises anthracene.